Fractional order electromagnetics

Authors:
J. A. Tenreiro Machado;Isabel S. Jesus;Alexandra Galhano;J. Boaventura Cunha
Affiliations:
Department of Electrical Engineering, Institute of Engineering of Porto, Porto, Portugal;Department of Electrical Engineering, Institute of Engineering of Porto, Porto, Portugal;Department of Electrical Engineering, Institute of Engineering of Porto, Porto, Portugal;University of Trás-os-Montes and Alto Douro, Engineering Department, Vila-Real, Portugal
Venue:
Signal Processing - Fractional calculus applications in signals and systems
Year:
2006

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Abstract

The Maxwell equations constitute a formalism for the development of models describing electromagnetic phenomena. The four Maxwell laws have been adopted successfully in many applications and involve only the integer order differential calculus. Recently, a closer look for the cases of transmission lines, electrical motors and transformers, that reveal the so-called skin effect, motivated a new perspective towards the replacement of classical models by fractional-order mathematical descriptions. Bearing these facts in mind this paper addresses the concept of static fractional electric potential. The fractional potential was suggested some years ago. However, the idea was not fully explored and practical methods of implementation were not proposed. In this line of thought, this paper develops a new approximation algorithm for establishing the fractional order electrical potential and analyzes its characteristics.